Shock and Vibration

Volume 2018, Article ID 4367201, 8 pages

https://doi.org/10.1155/2018/4367201

## A Nonparametric Method for Automatic Denoising of Microseismic Data

^{1}School of Resources and Safety Engineering, Central South University, Changsha, Hunan 410083, China^{2}Digital Mine Research Center, Central South University, Changsha, Hunan 410083, China

Correspondence should be addressed to Pingan Peng; moc.kooltuo@na_gnip

Received 5 January 2018; Accepted 13 February 2018; Published 16 July 2018

Academic Editor: Xinglin Lei

Copyright © 2018 Pingan Peng and Liguan Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Noise suppression or signal-to-noise ratio (SNR) enhancement is often desired for better processing results from a microseismic dataset. In this paper, we proposed a nonparametric automatic denoising algorithm for microseismic data. The method consists of three major steps: (1) applying a two-step AIC algorithm to pick P-wave arrival; (2) subtracting the noise power spectrum from the signal power spectrum; (3) recovering the microseismic signal by inverse Fourier transform. The proposed method is tested on synthetic datasets with different signal types and SNRs, as well as field datasets. The results of the proposed method are compared against ensemble empirical mode decomposition (EEMD) and wavelet denoising methods, which shows the effectiveness of the method for denoising and improving the SNR of microseismic data.

#### 1. Introduction

In the past few decades, microseismic monitoring has been widely used in a variety of applications, ranging from hydraulic fracturing to mining and geotechnical engineering [1, 2]. The signal is crucial for microseismic monitoring, and its quality will significantly affect the results of event detection, location, and source mechanism estimation. However, there are plenty of noise sources due to the complex situation of the project site, such as artificial activities, mechanical equipment, electrical interference, and equipment noise, which can severely affect the quality of the seismograms [3]. As a result, microseismic signals are often strongly contaminated by unwanted noise.

Noise suppression is a key step in microseismic data processing, aiming at improving the signal-to-noise ratio (SNR) [4]. Hence, numerous methods have been presented for this in the past few decades that can be classified into four main categories: (1) infinite impulse response (IIR) filters, known as low-pass, high-pass, band-pass, and band-stop filter (e.g., [5]); (2) Fourier-based filters (e.g., [6–8]); (3) EMD-based (empirical mode decomposition) filters (e.g., [9–14]); (4) wavelet-based filters (e.g., [15–17]).

Huang et al. [18] introduced the EMD algorithm to the signal processing community and it has been widely used since then. Bekara and Van der Baan [9] proposed a frequency-offset EMD technique to suppress the seismic random and coherent noise. In order to eliminate mode mixing present in the original EMD algorithm, ensemble empirical mode decomposition (EEMD) method has been recently proposed by Wu and Huang [19]. Han and van der Baan [10] developed a novel seismic and microseismic denoising method based on EEMD combined with adaptive thresholding. To et al. [20] compared Fourier-based and wavelet-based denoising techniques applied to geophysical data. Gaci [21] studied soft thresholding denoising techniques based on the discrete wavelet transform to enhance the first-arrival picking. In addition to Mousavi et al. [1], Mousavi and Langston [22] also used synchrosqueezed continuous wavelet transform (SS-CWT) for seismic denoising.

The aforementioned methods have played an important role in enhancing the quality of microseismic signals, but there is still room for SNR improvement. On the other hand, many of these methods have a large number of parameters, which must be tuned for each data set, and the goal of our work is to reduce the number of adjustable parameters that make the process more automatic.

In this paper, we introduce a nonparametric method for automatic denoising of microseismic data based on Akaike's Information Criterion (AIC) and Fourier transform, called PD (Pick & Denoise) method. In the following sections, a brief theoretical introduction to Akaike's Information Criterion and Fourier transform will be presented, as well as the details of our method. We analyze the performance of the proposed method applied to both synthetic and field microseismic data in terms of efficiency and signal preservation and contrast the results against standard EEMD and wavelet denoising methods.

#### 2. Theoretical Background and Development

##### 2.1. Akaike’s Information Criterion

AIC is one of the commonly used methods for P-wave arrival picking in both the seismic and microseismic field. It is assumed that a seismogram can be divided into locally stationary segments, each modeled as an autoregressive process, and that the intervals before and after the onset time are two different stationary processes [23]. The AIC function for seismogram of length* N* is defined as where is the* k*th sampling point, ; is the order of the autoregressive process; is a constant; and indicate the variance of the seismogram in the two intervals not explained by the autoregressive, respectively. Since the calculation of (1) is very complex, Maeda [24] proposed a simpler method as follows:where* var* represents the variance of the data, . The P-wave arrival is the corresponding point where the AIC has a minimum value.

AIC function will have a minimum value for any input. When SNR is relatively low, the global minimum cannot be guaranteed to indicate the P-wave arrival. Thus, the accuracy of Maeda’s AIC method depends heavily on the choice of the time window.

##### 2.2. Fourier Transform and Its Inverse Transform

Fourier transform is an important tool to convert the signal from time domain to frequency domain, and its inverse transform can be used to restore the signal from frequency domain to time domain. For signal , , the Fourier transform and its inverse transform can be expressed as

Because Discrete Fourier Transform (DFT) requires large computational cost, we generally reduce the amount of computation by decomposing the time series into odd and even subsequences by Fast Fourier transform (FFT).

For a signal of length (*M* is a positive integer; zero-padding is used if the signal length is insufficient), we split the* N*-point data sequence into two* N*/2-point data sequences and , corresponding to the even-numbered and odd-numbered samples of , respectively; that is,

Thus and are obtained by decimating by a factor of 2, and the above decimation-in-time decomposition can be performed -1 times, until each DFT is length 2. A length 2 DFT requires no multiplies, and the computational cost is evidently reduced. Finally, the N-point DFT can be expressed as follows:where is the rotation factor, is the DFT of the odd sequence, and is the DFT of the even sequence.

##### 2.3. The Proposed Method

A typical microseismic signal consists of three segments: the presignal noise, microseismic event, and background noise level, as shown in Figure 1. Normally, the microseismic event starts from the P-wave arrival and ends at the S coda, containing the key information of rock fracture. If we can extract the noise-related information from the presignal noise and then subtract this part from the entire signal, we can restore the original signal better. According to this idea, a nonparametric automatic denoising method is proposed for microseismic data as well as earthquake data that includes presignal noise.